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E-raamat: Introduction to Traveling Waves [Taylor & Francis e-raamat]

(College of Charleston, USA), (Miami University, USA), (Miami Univeristy, USA)
  • Formaat: 160 pages, 32 Line drawings, black and white; 32 Illustrations, black and white
  • Ilmumisaeg: 14-Nov-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003147619
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  • Taylor & Francis e-raamat
  • Hind: 143,10 €*
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  • Tavahind: 204,43 €
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Introduction to Traveling WavesSuurem pilt
  • Formaat: 160 pages, 32 Line drawings, black and white; 32 Illustrations, black and white
  • Ilmumisaeg: 14-Nov-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003147619
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003147619

This book focuses on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students.

 

 



Introduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. This book includes techniques that are not covered in those texts.

Through their experience involving undergraduate and graduate students in a research topic related to traveling waves, the authors found that the main difficulty is to provide reading materials that contain the background information sufficient to start a research project without an expectation of an extensive list of prerequisites beyond regular undergraduate coursework. This book meets that need and serves as an entry point into research topics about the existence and stability of traveling waves.

Features

  • Self-contained, step-by-step introduction to nonlinear waves written assuming minimal prerequisites, such as an undergraduate course on linear algebra and differential equations.
  • Suitable as a textbook for a special topics course, or as supplementary reading for courses on modeling.
  • Contains numerous examples to support the theoretical material.
    • Supplementary MATLAB codes available via GitHub.

    • Preface xi
    Chapter 1 Nonlinear traveling waves
    		1(26)
    1.1 Traveling Waves
    		1(4)
    1.2 Reaction-Diffusion Equations
    		5(3)
    1.3 Traveling Waves As Solutions Of Reaction-Diffusion Equations
    		8(4)
    1.4 Planar Waves
    		12(2)
    1.5 Examples Of Reaction-Diffusion Equations
    		14(7)
    1.5.1 Fisher-Kpp Equation
    		14(4)
    1.5.2 Nagumo Equation
    		18(3)
    1.6 Other Partial Differential Equations That Support Waves
    		21(6)
    1.6.1 Nonlinear Diffusion, Convection, And Higher Order Derivatives
    		21(1)
    1.6.2 Burgers Equation
    		21(1)
    1.6.3 Korteweg-De Vries (Kdv) Equation
    		22(5)
    Chapter 2 Systems Of Reaction-Diffusion Equations Posed On Infinite Domains
    		27(22)
    2.1 Systems Of Reaction-Diffusion Equations
    		27(4)
    2.2 Examples Of Reaction-Diffusion Systems
    		31(18)
    2.2.1 Fitzhugh-Nagumo System
    		31(3)
    2.2.2 Population Models
    		34(4)
    2.2.3 Belousov-Zhabotinski Reaction
    		38(3)
    2.2.4 Spread Of Infection Disease
    		41(1)
    2.2.5 The High Lewis Number Combustion Model
    		42(7)
    Chapter 3 Existence Of Fronts, Pulses, And Wavetrains
    		49(34)
    3.1 Traveling Waves As Orbits In The Associated Dynamical Systems
    		49(4)
    3.2 Dynamical Systems Approach: Equilibrium Points
    		53(5)
    3.3 Existence Of Fronts In Fisher-Kpp Equation: Trapping Region Technique
    		58(13)
    3.3.1 Existence Of Fronts In Nagumo Equation
    		64(5)
    3.3.2 Rotated Vector Fields And Existence Of A Heteroclinic Orbit Between A And C For Some C ≠ O
    		69(2)
    3.4 Existence Of Fronts In Solid Fuel Combustion Model
    		71(4)
    3.5 Wavetrains
    		75(8)
    Chapter 4 Stability Of Fronts And Pulses
    		83(66)
    4.1 Stability: Introduction
    		83(3)
    4.2 A Heuristic Presentation Of Spectral Stability For Front And Pulse Traveling Wave Solutions
    		86(23)
    4.2.1 Eigenvalue Problem
    		87(10)
    4.2.2 Spectrum And Spectral Stability
    		97(12)
    4.3 Location Of The Point Spectrum
    		109(35)
    4.3.1 Spectral Energy Estimates
    		109(10)
    4.3.2 Evans Function
    		119(1)
    4.3.2.1 Definition Of The Evans Function
    		119(6)
    4.3.2.2 Gap Lemma
    		125(1)
    4.3.2.3 Evans Function Computation: Scalar Equations
    		126(8)
    4.3.2.4 Evans Function Computation: Systems Of Equations
    		134(10)
    4.4 Beyond Spectral Stability
    		144(5)
    Bibliography 149(10)
    Index 159
    Anna R. Ghazaryan is a Professor of Mathematics at Miami University, Oxford, OH. She received her Ph.D. in 2005 from the Ohio State University. She is an applied analyst with research interests in applied dynamical systems, more precisely, traveling waves and their stability.

    Stéphane Lafortune is Professor of Mathematics at the College of Charleston in South Carolina. He earned his Ph.D. in Physics from the Université de Montréal and Université Paris VII in 2000. He is an applied mathematician who works on nonlinear waves phenomena. More precisely, he is interested in the theory of integrable systems and in the problems of existence and stability of solutions to nonlinear partial differential equations.

    Vahagn Manukian is an Associate Professor of Mathematics at Miami University. He obtained a M.A. Degree Mathematics from SUNY at Buffalo and a Ph.D. in mathematics from the Ohio State University in 2005. Vahagn Manukian uses dynamical systems methods such as local and global bifurcation theory to analyze singularly perturbed nonlinear reaction diffusions systems that model natural phenomena.
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